Math 4111, Fall, 2020

Dept. of Mathematics, Washington Univ.


Syllabus for Math 4111 

Real Analysis

Instructor: Steven G. Krantz

Classroom: The course will be taught OnLine only. No classroom.

e-mail address:

Office: 103, Cupples I

Office Hour: Monday, Wednesday, Friday from 2:00pm to 4:00pm, either by email or phone (510-875-8972).

Phone: (510) 875-8972

Dept. Office: 100, Cupples I

Dept. Phone: (314) 935-6760

Course Home Page:


Course Description: The purpose of this course is

to serve as a rigorous introduction to analysis on the real number system.

We construct the real numbers from scratch, and we prove their fundamental properties.

We study a number of important and famous theorems such as the Weierstrass approximation theorem,

the Weierstrass nowhere differentiable function, the intermediate value theorem,, and

and so forth. This class is hard work, and it is demanding. But it is worth it.




Textbook: S. G. Krantz, Real Analysis and Foundations,

4th edition, CRC Press, Boca Raton, FL, 2016.

Elements of the Course:

Homework: 25% of grade

Midterm Exam: (2 of these) each 25% of grade

Final Exam: 25% of grade

TOTAL: 100%


The homework is an essential part of this course. Each new idea

builds on previous ideas, so it is essential to master and internalize each

one when you encounter it. Be sure to do the homework in a regular and timely

fashion. Homework should be written out on 8.5" x 11" paper and submitted

on time. It will be graded. We will use the CrowdMark system for submitting

homework. What you will do then is scan your homework and submit it OnLine.

When a homework assignment is formulated, CrowdMark

will let you know and tell you how to submit..


Be familiar with this Web page. This is where homework assignments will be

posted, homework solutions posted, exam solutions posted, due dates will be posted,

and also where exams and other course events and information

will be announced.

We will decide when our midterm exams will be.

If there are particular days when you do not want an exam (for a religious

holiday or other reason), please let me know.

First Math 4111 Lecture, 09-14-2020

Second Math 4111 Lecture, 09-16-2020

Audio for Second Math 4111 Lecture, 09-16-2020

Third Math 4111 Lecture, 09-18-2020

Audio for Third Math 4111 Lecture, 09-18-2020

Fourth Math 4111 Lecture, 09-21-2020

Audio for Fourth Math 4111 Lecture, 09-21-2020

FIRST HOMEWORK ASSIGNMENT due Monday, September 28 at 11:59pm.

Section 1.1

1, 2, 3, 4, 5, 7, 11

Section 1.2

2, 3, 5, 7, 8, 9, 10, 13

Fifth Math 4111 Lecture, 09-23-2020

Audio for Fifth Math 4111 Lecture, 09-23-2020

Sixth Math 4111 Lecture, 09-25-2020

Audio for Sixth Math 4111 Lecture, 09-25-2020

SECOND HOMEWORK ASSIGNMENT due Monday, October 12 at 11:59pm.

Section 2.1:

1, 2, 3, 8, 10, 11, 12.

Section 2.2:

1, 2, 4, 8.

Seventh Math 4111 Lecture, 09-28-2020

Eighth Math 4111 Lecture, 09-30-2020

Ninth Math 4111 Lecture, 10-02-2020

Tenth Math 4111 Lecture, 10-05-2020